Orthotope sphere decoding method and apparatus for signal reconstruction in the multi-input multi-output antenna system

ABSTRACT

The present disclosure provides an orthotope sphere decoding method of a multiple antenna system. The method includes: tree mapping a node having highest pruning potential that can be predicted at a root of a tree of orthotope sphere decoding to a root level of the tree, among nodes to be mapped to the tree; and performing tree search of the orthotope sphere decoding on the nodes mapped to the tree.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority to Korean Patent Application No.10-2012-0093627 filed on 27 Aug. 2012 and all the benefits accruingtherefrom under 35 U.S.C. §119, the contents of which are incorporatedby reference in their entirety.

BACKGROUND

1. Technical Field

The present invention relates to an orthotope sphere decoding method forsignal reconstruction in a multiple antenna system and an apparatus forthe same, and more particularly, to an orthotope sphere decoding methodfor signal reconstruction in a multiple antenna system and an apparatusfor the same, in which, in order to place a node that is most probableto be pruned at a root of a tree before tree search for orthotope spheredecoding is performed in the multiple antenna system, pruning potentialis predicted, and each node is mapped to an orthotope tree according tothe pruning potential at each level, thereby reducing complexity ofdecoding for signal reconstruction.

2. Description of the Related Art

As high-quality and high-speed data transmission is required in awireless communication environment, a multiple-input and multiple-output(hereinafter, referred to as ‘MIMO’) system using a multiple antenna isused for efficient use of limited frequencies. The MIMO system can beoperated according to a space-time coding scheme or a space-divisionmultiplexing scheme. The space-time coding scheme is a technique capableof enhancing reliability of a wireless communication system by encodingdata transmitted from different antennas. The space-divisionmultiplexing scheme is a technique which increases data transmissionrates by simultaneously transmitting data independent from one anotherthrough multiple antennas.

Various techniques have been proposed to detect transmission symbolsfrom received symbols at a receiving end when the MIMO system transmitsindependent symbols through multiple transmission antennas in thespace-division multiplexing scheme. The maximum likelihood (ML)detection technique calculates and compares Euclidean distance for alltransmittable symbol vectors in order to detect the symbols.

The ML detection technique searches for transmission symbols having ashortest Euclidean distance from a received signal for all combinationsof transmittable transmission symbols. However, if the number ofantennas and the scale of a modulation m scheme increase, complexity ofthe ML detection is exponentially increased, and thus it is verydifficult to implement ML detection. In order to reduce the complexityof ML detection, a sphere decoding technique has been developed.

Since the sphere decoding technique calculates Euclidean distance onlyfor a set of symbol vectors existing in a sphere having a radius that isset in the initial stage considering noise variance and channel state,it can reduce the complexity of ML detection. However, complexity of asphere decoder varies depending upon initial radius and a method ofsearching for lattice vectors existing in a sphere. That is, if theinitial radius is set too large, numerous lattice vectors may existwithin the initial radius, and thus the sphere decoder will have acomplexity almost equal to that of an ML detector. In addition, if theinitial radius is too small, the sphere decoder is unable to search foran effective lattice vector. In addition, if SNR of the sphere decoderis low, the number of visiting nodes, i.e., complexity, abruptlyincreases when tree search is performed, and thus decoding efficiency isdegraded.

BRIEF SUMMARY

Therefore, the present invention is aimed at providing an orthotopesphere decoding method for signal reconstruction in a multiple antennasystem and an apparatus for the same, in which, in order to place a nodethat is most probable to be pruned at a root of a tree before treesearch for orthotope sphere decoding is performed in the multipleantenna system, pruning potential is predicted, and each node is mappedto an orthotope tree according to the pruning potential at each level,and thus complexity of decoding for signal reconstruction can bereduced.

One aspect of the present invention provides an orthotope spheredecoding method of a multiple antenna system, which includes: treemapping a node having highest pruning potential that can be predicted ata root of a tree of orthotope sphere decoding to a root level of thetree, among nodes to be mapped to the tree; and performing tree searchof the orthotope sphere decoding on the nodes mapped to the tree.

The tree mapping may include: receiving transmission symbols of themultiple antenna system; predicting pruning potential at the tree rootfor each node that will be mapped to the tree in correspondence to eachreceived transmission symbol; and placing a node having the highestpruning potential at the root level of the tree.

The predicting pruning potential may use, as the pruning potential, anumerical value which expresses possibility of a node to be pruned fromthe root of the tree through an OC-test.

The predicting pruning potential may use, as the pruning potential, anupper bound of the number of constellation points corresponding to eachsymbol of the node that will be pruned through the OC-test and removedthrough tree search.

The predicting pruning potential may include: calculating the number ofconstellation points within a radius of a threshold value set by theOC-test; and using, as the upper bound of the number of theconstellation points, a value calculated by subtracting the number ofconstellation points within the radius of the threshold value from thenumber of all constellation points in the node.

The set threshold value may have an orthotope radius containing at leastone constellation point within a radius from a center point of theorthotope.

If an O-metric of the constellation point satisfies the followingequation, the constellation point is within the radius of the setthreshold value, and otherwise, the constellation point is outside theradius of the set threshold value:Δ(s _(k))≦√{square root over (C _(min))}·δ_(k),

wherein

${C_{\min} = {\max\limits_{{k = 1},2,\mspace{11mu}\ldots\mspace{14mu},N}\left\lbrack {\left( \delta_{k}^{- 1} \right)^{2}{\min\limits_{s_{k} \in O}\left( {\Delta^{2}\left( s_{k} \right)} \right)}} \right\rbrack}},$δ_(k) denotes a k-th norm of an inverse channel matrix, s_(k) denotes aconstellation point, Δ(s_(k)) denotes the O-metric of s_(k), and kdenotes a level of an antenna.

The performing tree search may include performing the tree search byperforming pruning on the mapped tree through the OC-test.

The tree mapping may include: receiving transmission symbols of themultiple antenna system; performing prior tree mapping on nodescorresponding to the received transmission symbols in a predeterminedsequence of antennas; predicting the pruning potential at the tree rootfor each node in correspondence to each transmission symbol; and placinga node having the highest pruning potential at the root level of thepriorly tree mapped tree based on a result of the prediction.

The placing a node at the root level may include performing tree mappingby exchanging positions of the node having the highest pruning potentialand a node positioned at the root level of the priorly tree mapped tree.

The tree mapping may further include performing new tree mapping on thepriorly tree mapped tree in descending order of pruning potential basedon the result of the prediction.

Another aspect of the present invention provides an orthotope spheredecoding apparatus of a multiple antenna system, the apparatuscomprising: a tree mapping unit which performs tree mapping of a nodehaving highest pruning potential that can be predicted at a root of atree of orthotope sphere decoding to a root level of the tree, amongnodes to be mapped to the tree; and a tree search unit which performstree search of the orthotope sphere decoding on the nodes mapped to thetree.

The tree mapping unit may include: a reception unit which receivestransmission symbols of the multiple antenna system; a prediction unitwhich predicts pruning potential at the tree root for each node thatwill be mapped to the tree in correspondence to each receivedtransmission symbol; and a placement unit which places a node having thehighest pruning potential at the root level of the tree.

The prediction unit may use, as the pruning potential, a numerical valuewhich expresses possibility of a node to be pruned from the root of thetree through an OC-test.

The prediction unit may use, as the pruning potential, an upper bound ofthe number of constellation points corresponding to each symbol of thenode that will be pruned through the OC-test and removed through thetree search.

The prediction unit may calculate the number of constellation pointswithin a radius of a threshold value set by the OC-test; and use, as theupper bound of the number of the constellation points, a valuecalculated by subtracting the number of constellation points within theradius of the threshold value from the number of all constellationpoints in the node.

According to the present invention, tree mapping is performed by placinga node having the highest pruning potential at a root of a tree, andthus more subordinate nodes can be pruned when the corresponding node ispruned in the process of tree search. Accordingly, the number of nodesto visit for tree search is reduced, and thus decoding performance ofsignal reconstruction can be improved in a multiple antenna system.

Further, since complexity of a receiver can be reduced while maintainingperformance of a maximum likelihood (ML) receiver, the high-speed datatransmission function, which is an advantage of the multiple antennasystem, can be further improved, and thus data transmission rates can beimproved in a variety of wireless and mobile communication fields.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other aspects, features, and advantages of the inventionwill become apparent from the detailed description of the followingembodiments in conjunction with the accompanying drawings, in which:

FIG. 1 is a block diagram of a multiple antenna system in accordancewith one embodiment of the present invention;

FIG. 2 is a view showing an input space and an output space fororthotope sphere decoding in accordance with one embodiment of thepresent invention;

FIG. 3 is a view of constellation points on a minimum orthotope inorthotope sphere decoding in accordance with one embodiment of thepresent invention;

FIG. 4 is a view of a tree structure used for tree search in orthotopesphere decoding in accordance with one embodiment of the presentinvention;

FIG. 5 is a view of an orthotope sphere decoder for signalreconstruction of a multiple antenna system in accordance with oneembodiment of the present invention;

FIG. 6 is a flowchart of an orthotope sphere decoding method inaccordance with one embodiment of the present invention;

FIG. 7 is a flowchart of a tree mapping operation of an orthotope spheredecoding method in accordance with one embodiment of the presentinvention;

FIG. 8 is a flowchart of a potential prediction operation of anorthotope sphere decoding method in accordance with one embodiment ofthe present invention;

FIG. 9 is a flowchart of a tree mapping operation of an orthotope spheredecoding method in accordance with another embodiment of the presentinvention; and

FIG. 10 is a flowchart of a tree mapping operation of an orthotopesphere decoding method in accordance with a further embodiment of thepresent invention.

DETAILED DESCRIPTION

Exemplary embodiments of the present invention will now be described indetail with reference to the accompanying drawings. However, it shouldbe understood that the present invention is not limited to the followingembodiments and may be embodied in different ways by those skilled inthe art without departing from the scope of the present invention.Further, it should be understood that various modifications andequivalent embodiments may be made by those skilled in the art withoutdeparting from the spirit and scope of the present invention. In thedrawings, the thicknesses of layers and regions can be exaggerated oromitted for clarity. The same components will be denoted by the samereference numerals throughout the specification.

FIG. 1 is a block diagram showing the configuration of a multipleantenna system in accordance with one embodiment of the presentinvention.

Referring to FIG. 1, a multiple antenna system in accordance with oneembodiment of the present invention includes a transmitter 10 fortransmitting independent symbols through a plurality of transmissionantennas and a receiver 20 for detecting transmission symbols fromreception symbols received through a plurality of reception antennas.

The transmitter 10 encodes and interleaves a bit stream corresponding toan input signal to be transmitted, and converts the bit stream in seriesand in parallel according to the number of antennas. Lattice symbolsconverted in parallel are simultaneously transmitted through multipleantennas. The receiver 20 receives the lattice type symbols transmittedfrom the plurality of antennas provided in the transmitter 10, detects aplurality of independent transmission symbols included in the receivedsymbols, and outputs a detection signal. The receiver 20 includes anorthotope sphere decoder 200 for detecting the transmission symbols. Theorthotope sphere decoder 200 searches for transmission symbols having aminimum Euclidean distance for lattice vectors existing in a spherehaving a predetermined initial radius.

FIG. 2 is a view showing an input space and an output space fororthotope sphere decoding according to the embodiment of the presentinvention. Each of the symbols in the figure represents a 16-QAMconstellation point.

When the number of antennas of the receiver 20 is M and the number ofantennas of the transmitter 10 is N in the multiple antenna system, achannel model of the multiple antenna system can be expressed asfollows:r=Hs+n

wherein r=[r₁, . . . , r_(M)]^(T) denotes received signals. H denotes anM×N block Rayleigh fading channel matrix. Each entry of H is a Gaussiandistributed random variable of an IID (independently and identicallydistributed) complex number control-mean unit. Here, the channel matrixis a value provided by the receiver 20. s=[s₁, . . . , s_(N)]^(T)denotes symbol vectors transmitted from the transmitter 10 and satisfies

ε

^(N)⊂

^(N). Here,

denotes constellation points of a signal in complex number domain

. n=[n₁, . . . , n_(M)]^(T) denotes AWGN (additive white Gaussian noise)vectors and has zero-mean and variance ρ².

The orthotope sphere decoder according to the embodiment is applied tolattice Hs (

ε

^(N)⊂

^(N)) having a complex number.

H(k,:) denotes the k-th row of matrix H. H^(†) denotes inverse numbersof matrix H. Each component of the vector is expressed as a subscript.For example, s_(k) denotes k-th component of vector S.

denotes cardinality of set

. ∥s∥ denotes the second norm of vector S.

denotes a complex number domain.

In orthotope sphere decoding, additional constraints are applied tosphere decoding.

A tree search is performed in the sphere decoding. QR decomposition isperformed on matrix H in sphere decoding. The sphere decoding does notcalculate a full Euclidean distance and examines whether or notconstellation points are within a certain sphere radius √{square rootover (C)} using a partial matrix. These conditions are referred to assphere constraints (SCs) and can be expressed as follows:

$d_{k} = {{\sum\limits_{i = k}^{N}{q_{i}}^{2}} \leq C}$

wherein d_(k) denotes a square root of a partial Euclidean distance atthe k-th level (1≦k≦N). q_(i) denotes the i-th component of q=R(x−s). Atthis point, R denotes the upper triangular matrix in QR decomposition ofmatrix H. x=H^(†)i*.

The concept of the orthotope can be specified through parameters oforthotope square width (OSW). The orthotope can be specified as acollection of center points x=[x₁, x₂, . . . , x_(N)]^(T) and widths ofspaces w=[w₁, w₂, . . . , w_(N)]^(T) restricting the orthotope. Theconcept of the orthotope is extended to the complex plane so as toexplain each dimension of the orthotope using the complex plane insteadof the spaces. Accordingly, two space widths can be used for real andimaginary numbers in order to restrict each complex plane of theorthotope.H:={c∥

(c _(i) −x _(i))|≦w _(i),|ℑ(c _(i) −x _(i))|≦w _(i) ,c _(i) ,x _(i) ε

,w _(i)ε

,1≦i≦N}

Each dimension of the orthotope is a square.

The orthotope square width (OSW) can be expressed as δ₁, δ₂, . . . ,δ_(N) (δ_(k)=∥H^(†)(k,:)∥) and is proportional to the widths of theorthotope squares. The widths of the orthotope squares are OSWs andmaintain the same relative proportionality. This is referred to as anOSW constraint.

An O-metric can be used to examine whether or not constellation points_(k) is inside the orthotope. The O-metric is obtained by measuring howfar a constellation point is positioned from the center of pertinentorthotope square x_(k). O-metric Δ(s_(k)) of a candidate constellationpoint s_(k) is a minimum square width containing the constellation pointwithin the boundary thereof and can be expressed as the followingequation:Δ(s _(k))=max{|

(s _(k))−

(x _(k))|,|ℑ(s _(k))−ℑ(x _(k))|}

wherein

(s_(k)) is the real number part of s_(k), and ℑ(s_(k)) is the imaginarynumber part of s_(k).

If the O-metric of a certain constellation point s_(k) is smaller thanthe k-th orthotope square width, the constellation point is inside theorthotope. This is referred to as an orthotope constraint (OC) and canbe expressed as a mathematical shown below.Δ(s _(k))≦√{square root over (C)}·δ _(k) for k=1, . . . ,N

The degree of pruning accomplished through an OC test depends on theconstraints applied to the size of the orthotope. The smaller theorthotope is, the better the pruning will be. In order to accomplish thebest pruning, a minimum orthotope needs to be selected while using theML technique. Vector points existing inside the minimum orthotope arenot pruned through the OC test, because these points are inside theorthotope which always passes the OC test. The points or symbolsexisting inside the orthotope at each level are referred to asunavoidable constellation points (UCPs). If the unavoidableconstellation points are determined at each level, the number ofconstellation points that will be pruned at each level is calculated bysubtracting the number of unavoidable constellation points from thetotal number constellation points.

The unavoidable constellation points with respect to s_(k) are insidethe k-th square of the minimum orthotope including the ML solution.However, the exact number of the unavoidable constellation points cannotbe acquired until the tree search is completed since the OC test forconfirming the unavoidable constellation points is required to haveknowledge about the radius of the minimum hyper-sphere including the MLsolution. That is, it is the Euclidean distance of the ML solution forreceived signal r.

Instead, a lower bound of the number of unavoidable constellation pointscan be used. In order to find the lower bound, a minimum orthotopecontaining at least one vector point which does not need to be an MLsolution can be selected. This orthotope is referred to as a minimumorthotope (MO).

The minimum orthotope has a center at x=H^(†)r, and this is the smallestorthotope containing at least one vector Sε◯^(N). There is one orthotopeat each level, and the orthotope includes N squares. Each square of theminimum orthotope should contain at least one constellation point. Thisis referred to as a minimum orthotope-level constraint. In addition, thesquares of the minimum orthotope should satisfy the OSW constraints.

Therefore, the squares inside the minimum orthotope should satisfy boththe MO-level constraints and the OSW constraints. In addition, noorthotope can be smaller than the minimum orthotope and should containone constellation point. The constellation points inside the minimumorthotope are confirmed before tree search is started.

A constellation point where O-metric Δ(s_(k)) satisfies the test shownbelow is inside the minimum orthotope.

${\Delta\left( s_{k} \right)} \leq {\sqrt{C_{\min}} \cdot {\delta_{k}\left( {{Here},{C_{\min} = {\max\limits_{{k = 1},2,\mspace{11mu}\ldots\mspace{14mu},N}\left\lbrack {\left( \delta_{k}^{- 1} \right)^{2}{\min\limits_{s_{k} \in O}\left( {\Delta^{2}\left( s_{k} \right)} \right)}} \right\rbrack}}} \right)}}$S_(kd k) denotes the k-th norm of an inverse channel matrix, s_(k)denotes a constellation point, Δ(s_(k)) denotes the O-metric of s_(k),and k denotes a level of an antenna.

FIG. 3 is a view of constellation points on a minimum orthotope inorthotope sphere decoding in accordance with one embodiment of thepresent invention.

FIG. 3( a) shows a minimum required width for each level of the minimumorthotope in the orthotope sphere decoding according to the presentembodiment of the invention. FIG. 3( b) shows a minimum required s_(k)radius for each level. FIG. 3( c) shows the minimum orthotope.

The minimum orthotope of the orthotope sphere decoding will be describedwith reference to FIG. 3. In the figure, 16-QAM constellation points areused. The minimum width of a square needed at each level is obtainedaccording to the MO-level constraints, i.e.,

$\min\limits_{s_{k} \in O}{\left( {\Delta\left( s_{k} \right)} \right).}$This confirms that each square has at least one constellation pointtherein. Next, a minimum radius required for each level can becalculated using

$\left( \delta_{k}^{- 1} \right){\min\limits_{s_{k} \in O}{\left( {\Delta\left( s_{k} \right)} \right).}}$Next, in order to establish a minimum orthotope satisfying the OSWconstraints, a maximum radius should be selected from a set of minimumrequired radiuses as shown in

$\sqrt{C_{\min}} = {\max\limits_{{k = 1},2,\mspace{11mu}\ldots\mspace{14mu},N}{\left\lbrack {\left( \delta_{k}^{- 1} \right){\min\limits_{s_{k} \in O}\left( {\Delta\left( s_{k} \right)} \right)}} \right\rbrack.}}$If a square is set according to √{square root over (C_(min))}·δ_(k), theOSW constraints will be satisfied. As shown in FIG. 3, there are one ormore constellation points inside the squares. In this embodiment, thereis one constellation point at level 1, four constellation points atlevel 2, and two constellation points at level N because most of squaresin the orthotope contain more constellation points as they grow biggerto satisfy the OSW constraints. The number of constellation points ineach square of the orthotope is determined based on the center point Xand the OSW.

In addition to confirming the constellation points exiting inside theminimum orthotope, an upper bound of the number of constellation pointsthat can be pruned at each level can be determined This is referred toas pruning potential at each level. The pruning potential at each levelcan be obtained using the number of constellation points inside theminimum orthotope.

FIG. 4 is a view of a tree structure used for tree search in orthotopesphere decoding in accordance with one embodiment of the presentinvention.

Referring to FIG. 4, a BPSK modulation scheme used in the multipleantenna system having four antennas is described as an example. The fourantennas configure four levels in a tree.

The orthotope sphere decoder 200 in accordance with one embodiment ofthe present invention performs tree search on a tree which has nodescorresponding to transmission symbols. Leaves of the tree represent allcandidate symbol vectors that can be mapped to the tree.

The orthotope sphere decoder 200 performs tree search by visiting thenodes on a path reaching to a leaf node from a root of a tree in thedepth-first method.

The orthotope sphere decoder 200 detects transmission symbols byperforming an OC-test or an SC-test on each node in the process ofsearching the tree.

At this point, if an orthotope is smaller than the minimum orthotope setby performing the OC-test or the SC-test, the search is not continuedbelow the corresponding node, and the search flow moves to an upperlevel. If the search is not continued to subordinate nodes, this isreferred to as pruning. In order to perform the OC-test or the SC-test,an O-metric or a PED should be calculated at each node.

A square root of the PED is calculated at each node to perform theSC-test while visiting the node. If a node does not pass the SC-test,leaves of the node are highly probable not to pass the SC-test.Accordingly, the nodes subordinate to the corresponding nodes are prunedfrom the tree.

Most of the PED calculation for performing the SC-test is complex numberoperations while the sphere decoding search is performed. The PEDcalculation at the k-th level of the tree needs 8(N−k)+11 floating pointoperations (1≦k≦N). If some of the PED calculation can be removed,complexity of the sphere decoding can be reduced.

The orthotope sphere decoder 200 in accordance with one embodiment ofthe present invention performs optimum tree mapping in order to reducethe burden of calculating the O-metric or the PED at each node when treesearch is performed.

To this end, the orthotope sphere decoder 200 predicts and calculatespotential of a node to be pruned from the tree when the node is at theroot, by performing the OC-test at each node. Then, a node having thelargest potential among the predicted and calculated potentials isplaced at the root of the tree.

If a node having the highest pruning potential is placed at the root ofthe tree, further more subordinate nodes can be pruned when thecorresponding node is pruned in the process of tree search. Accordingly,the number of nodes to visit in the tree search is reduced. If thenumber of nodes to visit in the tree search is reduced, operations forcalculating the O-metric and the PED are reduced when the OC-test isperformed. If operations for calculating the O-metric and the PED arereduced, performance of the orthotope sphere decoding can be improved.

FIG. 5 is a view of an orthotope sphere decoder for signalreconstruction of a multiple antenna system in accordance with oneembodiment of the present invention.

Referring to FIG. 5, the sphere decoder 200 of a multiple antenna systemin accordance with one embodiment of the present invention includes atree mapping unit 210 and a tree search unit 220.

The tree mapping unit 210 tree maps a node having the highest pruningpotential that can be predicted at a root of a tree to the root level ofthe tree, among the nodes to be mapped to the tree of the orthotopesphere decoding.

The tree search unit 220 performs tree search of the orthotope spheredecoding for the tree mapped nodes. The tree search unit 220 can performthe tree search by performing pruning on the tree mapped by the treemapping unit 210, through the OC-test.

The mapping unit 210 may include a reception unit 211, a prediction unit212 and a placement unit 213.

The reception unit 211 receives transmission symbols of the multipleantenna system transmitted from the antennas of the transmitter 10.

The prediction unit 212 predicts pruning potential at the tree root foreach node that will be mapped to the tree in correspondence to eachreceived transmission symbol.

The prediction unit 212 may use, as the pruning potential, a numericalvalue which expresses possibility of a node to be pruned from the rootof the tree through the OC-test.

The prediction unit 212 may use, as the pruning potential, an upperbound of the number of constellation points corresponding to each symbolof a node that will be pruned through the OC-test and removed throughtree search.

The prediction unit 212 calculates the number of constellation pointswithin the radius of a threshold value set by the OC-test.

The prediction unit 212 may use, as the upper bound of the number of theconstellation points, a value calculated by subtracting the number ofconstellation points within the radius of a threshold value from thetotal number of constellation points in the node.

The threshold value may have an orthotope radius containing at least oneconstellation point within the radius from the center point of theorthotope.

If the constellation point satisfies the following equation, it iswithin the radius of the set threshold value, and otherwise, it is outof the radius of the set threshold value.Δ(s _(k))≦√{square root over (C _(min))}·δ_(k)  [Equation]

wherein

${C_{\min} = {\max\limits_{{k = 1},2,\mspace{11mu}\ldots\mspace{14mu},N}\left\lbrack {\left( \delta_{k}^{- 1} \right)^{2}{\min\limits_{s_{k} \in O}\left( {\Delta^{2}\left( s_{k} \right)} \right)}} \right\rbrack}},$δ_(k) denotes the k-th norm of an inverse channel matrix, s_(k) denotesa constellation point, Δ(s_(k)) denotes the O-metric of s_(k), and kdenotes a level of an antenna.

The placement unit 213 places a node having the highest pruningpotential at the root level of the tree.

FIG. 6 is a flowchart of an orthotope sphere decoding method inaccordance with one embodiment of the present invention.

Referring to FIG. 6, in S10 of the orthotope sphere decoding methodaccording to one embodiment, the tree mapping unit 210 tree maps a nodehaving the highest pruning potential that can be predicted at a root ofa tree to the root level of the tree, among the nodes to be mapped tothe tree of the orthotope sphere decoding.

In S20, the tree search unit 220 performs tree search of the orthotopesphere decoding for the nodes tree mapped by the tree mapping unit 210.

FIG. 7 is a flowchart of a tree mapping operation of an orthotope spheredecoding method in accordance with one embodiment of the presentinvention.

Referring to FIG. 7, in the tree mapping operation of the orthotopesphere decoding method according to the present embodiment, thereception unit 211 receives transmission symbols of the multiple antennasystem in S111.

In S112, the prediction unit 212 predicts pruning potential at the treeroot for each node that will be mapped to the tree in correspondence toeach transmission symbol received by the reception unit 211.

In S112, the prediction unit 212 may use, as the pruning potential, anumerical value which expresses possibility of a node to be pruned fromthe root of the tree through the OC-test in order to predict the pruningpotential.

In S112, the prediction unit 212 may use, as the pruning potential, anupper bound of the number of constellation points corresponding to eachsymbol of a node that will be pruned through the OC-test and removedthrough tree search in order to predict the pruning potential.

In S113, the placement unit 213 places a node having the highest pruningpotential at the root level of the tree.

FIG. 8 is a flowchart of a potential prediction operation of anorthotope sphere decoding method in accordance with one embodiment ofthe present invention.

Referring to FIG. 8, in the potential prediction operation of theorthotope sphere decoding method according to the present embodiment,the prediction unit 212 calculates the number of constellation pointswithin the radius of a threshold value set by the OC-test in S1121.

In S1122, the prediction unit 212 uses, as the upper bound of the numberof the constellation points, a value calculated by subtracting thenumber of constellation points within the radius of a threshold valuefrom the total number of constellation points in the node.

Here, the set threshold value may have an orthotope radius containing atleast one constellation point within the radius from the center point ofthe orthotope.

If the constellation point satisfies the following equation, it iswithin the radius of the set threshold value, and otherwise, it is outof the radius of the set threshold value:Δ(s _(k))≦√{square root over (C _(min))}·δ_(k)  [Equation]wherein

$\left. {C_{\min} = {\max\limits_{{k = 1},2,\mspace{11mu}\ldots\mspace{14mu},N}\left\lbrack {\left( \delta_{k}^{- 1} \right)^{2}{\min\limits_{s_{k} \in O}\left( {\Delta^{2}\left( s_{k} \right)} \right)}} \right\rbrack}} \right)$δ_(k) denotes the k-th norm of an inverse channel matrix, s_(k) denotesa constellation point, Δ(s_(k)) denotes the O-metric of, and s_(k)denotes a level of an antenna.

FIG. 9 is a flowchart of a tree mapping operation of an orthotope spheredecoding method in accordance with another embodiment of the presentinvention.

Referring to FIG. 9, in the tree mapping operation of the orthotopesphere decoding method in accordance with the present embodiment, thereception unit 211 receives transmission symbols of the multiple antennasystem in S121.

In S122, the placement unit 213 performs prior tree mapping on the nodescorresponding to the received transmission symbols in a predeterminedsequence of antennas.

In S123, the prediction unit 212 predicts pruning potential at the treeroot for each node that will be mapped to the tree in correspondence toeach transmission symbol.

In S124, the placement unit 213 places a node having the highest pruningpotential at the root level of the priorly tree mapped tree based on aresult of the prediction of the prediction unit 212.

In S125, the placement unit 213 places the node positioned at the rootlevel of the priorly tree mapped tree to the position where the nodehaving the highest pruning potential is placed.

That is, the placement unit 213 may perform tree mapping by exchangingpositions of the node having the highest pruning potential and the nodepositioned at the root level of the priorly tree mapped tree.

FIG. 10 is a flowchart of a tree mapping operation of an orthotopesphere decoding method in accordance with a further embodiment of thepresent invention.

Referring to FIG. 10, in the tree mapping operation of the orthotopesphere decoding method in accordance with the present embodiment, thereception unit 211 receives transmission symbols of the multiple antennasystem in S131.

In S132, the placement unit 213 performs prior tree mapping on the nodescorresponding to the received transmission symbols in a predeterminedsequence of antennas.

In S133, the prediction unit 212 predicts pruning potential at the treeroot for each node that will be mapped to the tree in correspondence toeach transmission symbol.

In S134, the placement unit 213 places a node having the highest pruningpotential at the root level of the priorly tree mapped tree based on aresult of the prediction of the prediction unit 212.

In S135, the placement unit 213 performs new tree mapping on the priorlytree mapped tree in descending order of pruning potential.

Although some exemplary embodiments have been described herein, itshould be understood by those skilled in the art that these embodimentsare given by way of illustration only, and that various modifications,variations and alterations can be made without departing from the spiritand scope of the invention. The scope of the present invention should bedefined by the appended claims and equivalents thereof.

What is claimed is:
 1. An orthotope sphere decoding method of a multipleantenna system, comprising: tree mapping a node having highest pruningpotential that can be predicted at a root of a tree of orthotope spheredecoding to a root level of the tree, among nodes to be mapped to thetree; and performing tree search of the orthotope sphere decoding on thenodes mapped to the tree, wherein the tree mapping comprises: receivingtransmission symbols of the multiple antenna system; predicting pruningpotential at the tree root for each node that will be mapped to the treein correspondence to each received transmission symbol; and placing anode having the highest pruning potential at the root level of the tree,and wherein the predicting pruning potential uses, as the pruningpotential, a numerical value which expresses possibility of a node to bepruned from the root of the tree through an orthotope constraint test(OC-test), and wherein the predicting pruning potential uses, as thepruning potential, an upper bound of the number of constellation pointscorresponding to each symbol of the node that will be pruned through theOC-test and removed through tree search.
 2. The orthotope spheredecoding method according to claim 1, wherein the predicting pruningpotential comprises: calculating the number of constellation pointswithin a radius of a threshold value set by the OC-test; and using, asthe upper bound of the number of the constellation points, a valuecalculated by subtracting the number of constellation points within theradius of the threshold value from the total number of constellationpoints in the node.
 3. The orthotope sphere decoding method according toclaim 2, wherein the set threshold value is a minimum orthotopethreshold value having an orthotope radius containing at least oneconstellation point within a radius from a center point of theorthotope.
 4. The orthotope sphere decoding method according to claim 3,wherein, if an O-metric of the constellation point satisfies thefollowing equation, the constellation point is within the radius of theset threshold value, and otherwise, the constellation point is outsidethe radius of the set threshold value:Δ(s _(k))≦√{square root over (C _(min))}·δ_(k), wherein${C_{\min} = {\max\limits_{{k = 1},2,\mspace{11mu}\ldots\mspace{14mu},N}\left\lbrack {\left( \delta_{k}^{- 1} \right)^{2}{\min\limits_{s_{k} \in O}\left( {\Delta^{2}\left( s_{k} \right)} \right)}} \right\rbrack}},$δ_(k) denotes a k-th norm of an inverse channel matrix, s_(k) denotes aconstellation point, Δ(s_(k)) denotes an O-metric of s_(k), and kdenotes a level of an antenna.
 5. The orthotope sphere decoding methodaccording to claim 1, wherein the performing tree search comprisesperforming the tree search by performing pruning on the mapped treethrough the OC-test.
 6. An orthotope sphere decoding method of amultiple antenna system, comprising: tree mapping a node having highestpruning potential that can be predicted at a root of a tree of orthotopesphere decoding to a root level of the tree, among nodes to be mapped tothe tree; and performing tree search of the orthotope sphere decoding onthe nodes mapped to the tree, wherein the tree mapping comprises:receiving transmission symbols of the multiple antenna system;performing prior tree mapping on nodes corresponding to the receivedtransmission symbols in a predetermined sequence of antennas; predictingthe pruning potential at the tree root for each node in correspondenceto each transmission symbol; and placing a node having the highestpruning potential at the root level of the priorly tree mapped treebased on a result of the prediction, and wherein the placing a node atthe root level comprises performing tree mapping by exchanging positionsof the node having the highest pruning potential and a node positionedat the root level of the priorly tree mapped tree.
 7. An orthotopesphere decoding method of a multiple antenna system, comprising: treemapping a node having highest pruning potential that can be predicted ata root of a tree of orthotope sphere decoding to a root level of thetree, among nodes to be mapped to the tree; and performing tree searchof the orthotope sphere decoding on the nodes mapped to the tree,wherein the tree mapping comprises: receiving transmission symbols ofthe multiple antenna system; performing prior tree mapping on nodescorresponding to the received transmission symbols in a predeterminedsequence of antennas; predicting the pruning potential at the tree rootfor each node in correspondence to each transmission symbol; and placinga node having the highest pruning potential at the root level of thepriorly tree mapped tree based on a result of the prediction, andwherein the tree mapping further comprises performing new tree mappingon the priorly tree mapped tree in descending order of pruning potentialbased on the result of the prediction.
 8. An orthotope sphere decodingapparatus of a multiple antenna system, the apparatus comprising: a treemapping unit which performs tree mapping of a node having highestpruning potential that can be predicted at a root of a tree of orthotopesphere decoding to a root level of the tree, among nodes to be mapped tothe tree; and a tree search unit which performs tree search of theorthotope sphere decoding on the nodes mapped to the tree, wherein thetree mapping unit includes: a reception unit which receives transmissionsymbols of the multiple antenna system; a prediction unit which predictspruning potential at the tree root for each node that will be mapped tothe tree in correspondence to each received transmission symbol; and aplacement unit which places a node having the highest pruning potentialat the root level of the tree, and wherein the prediction unit uses, asthe pruning potential, a numerical value which expresses possibility ofa node to be pruned from the root of the tree through an orthotopeconstraint test (OC-test), and wherein the prediction unit uses, as thepruning potential, an upper bound of the number of constellation pointscorresponding to each symbol of the node that will be pruned through theOC-test and removed through tree search.
 9. The orthotope spheredecoding apparatus according to claim 8, wherein the prediction unitcalculates the number of constellation points within a radius of athreshold value set by the OC-test; and uses, as the upper bound of thenumber of the constellation points, a value calculated by subtractingthe number of constellation points within the radius of the thresholdvalue from the total number of constellation points in the node.